C HAPTER 1 F RACTIONS AND D ECIMALS

Transcription

1 C HAPTER 1 F RACTIONS AND D ECIMALS Learning Outcomes 1-1 Compare the values of fractions in various formats. 1- Accurately add, subtract, multiply, divide fractions. 1- Convert fractions to mixed numbers decimals. 1- Recognize the format of decimals measure their relative values. 1- Accurately add, subtract, multiply, divide decimals. 1- Round decimals to the nearest tenth, hundredth, or thousth. Chapter Outline 1-1 Fractions Mixed Numbers 1- Equivalent Fractions 1- Simplifying Fractions to Lowest Terms 1- Finding Common Denominators 1- Comparing Fractions 1- Adding Fractions 1- Subtracting Fractions 1- Multiplying Fractions 1- Dividing Fractions 1- Working with Decimals 1-11 Rounding Decimals 1-1 Converting Fractions into Decimals 1-1 Converting Decimals into Fractions 1-1 Adding Subtracting Decimals 1-1 Multiplying Decimals 1-1 Dividing Decimals Lesson Plan Anticipatory Set The Numbers Game. Write, 1, 0., 1. on the board explain the basic difference between fractions, mixed numbers, decimals. Next write 1,,,,, 0 on the board or screen. Ask the students to use these numbers to create as many fractions, mixed numbers, decimals as possible in 0 seconds. Have the students compare numbers with each other. You may want to make it a contest bring a small prize for the student who creates the most. Explain to students that they will learn how to work with fractions, mixed numbers, decimals to perform dosage calculations. Teaching Strategies Assign collect the homework for Chapter 1. Check the student s answers to discover the topics within the chapter that require the most focused attention during class time. Have a health care professional visit the class discuss their role in dosage calculations as well as the importance of math accuracy preventing medication errors in the health care profession. Have students review the key terms for Chapter 1 using the Audio glossary Key Term Concentration game on the student CD. Have students in groups of three; review their basic math skills using the Math Challenge game on the student CD. Encourage students to complete each review practice section in the text/workbook check their answers. You can also remove the answers from the back of the book use the review practice questions as a graded assignment. Use the Critical Thinking on the Job Activities from Chapter 1 as Think-Pair-Share assignments in class. Have student groups discuss their answers present to the rest of the class. Use the PowerPoint presentation for Chapter 1, found on the student instructor resource CD-ROM, for a class lecture /or review. Use the Test Your Knowledge questions for discussion. Instructor s Manual for Math Dosage Calculations for Health Care 1

2 The online learning center at MathDosagee contains additional activities for each chapter. Links for the Internet activities from at the end of this chapter are provided on this site. Have students navigate to this site to complete the Internet activities. Play the Spin the Wheel on the student CD with individual, small groups or within the classroom in preparation for the final evaluation. Assess Use the Additional Exercises for Chapter 1 found at the end of this document for reinforcement of chapter concepts. These exercises can also be used as chapter quizzes. Students should complete each student CD activity when directed within the text. Have students save, print, or their completed Progress Report from the student CD for Chapter 1. The chapter review should be completed checked in preparation for the final chapter evaluation. Using the EZTest test bank for Chapter 1, create a written test in two versions for a final evaluation of student s proficiency. Access the Instructor s Manual documents in electronic format modify to match your curriculum needs. Use the chapter images labels to create your own worksheets, tests, or PowerPoint presentations. C HAPTER 1 Solutions 1-1 Fractions Mixed Numbers part type A blood whole whole group 1 part whole not type A blood whole group. part diabetic patients whole whole group 0 part whole not diabetic patients whole group _ is sixteen divided by three, or _ 1. 1 is four divided by fifteen, or 1. is three divided by, or. Because 1 1, Because, 1 c. Because 1 0, _ Because, 1 Because 0, 0 0 c. Because 1 1, R1 remainder denominator 1 1 R remainder denominator 1 _ R0 0 The remainder is zero, _ _ R0 The remainder is zero, 0_ Instructor s Manual for Math Dosage Calculations for Health Care

3 R remainder denominator 1 1 _ 1 remainder denominator 1 R1 _ 1 _ R 1 remainder denominator _ 1 0_ _ _ _ 11. _ Equivalent Fractions For Exercises 1, answers may vary _ _ _ _ 1 Instructor s Manual for Math Dosage Calculations for Health Care

4 _ _ _ ? 1. 1? 1. 1 _? _ ? ? _ ? ? 1. 1? ? 0. 1? _ 1- Simplifying Fractions to Lowest Terms Instructor s Manual for Math Dosage Calculations for Health Care

5 . cannot be reduced any further.. cannot be reduced any further cannot be reduced any further Finding Common Denominators 1. multiples of :,,, 1, 1, 1, 1, multiples of :, 1, 1, 1 is the LCD multiples of :,, 1, 0,, 0,, 0, multiples of :, 1,,, 0, 0 is the LCD multiples of :, 0,, 0, 1,, 1, 00 multiples of 0: 0, 0,,, is the LCD multiples of :,, multiples of :, is the LCD multiples of :,,,,, 1 multiples of 1: 1 1 is the LCD. already has the LCD as its denominator multiples of :, 1, 1 multiples of 1: 1 1 is the LCD. 1 1 already has the LCD as its denominator. 1. multiples of :, 1, 1,, 0,, multiples of :, 1, 1,,, is the LCD.. multiples of :, multiples of : is the LCD. is an equivalent fraction that already has the LCD as its denominator. Instructor s Manual for Math Dosage Calculations for Health Care

6 . multiples of :, 1,, multiples of : The LCD is. 1 is an equivalent fraction that already has the LCD as its denominator.. multiples of :,,, multiples of : The LCD is. 0 is an equivalent fraction that already has the LCD as its denominator. 11. multiples of :,, 1, 0,, 0,, 0,, 0, multiples of 11: 11,,,, The LCD is _ 1. multiples of :, 1 multiples of 1: 1 The LCD is 1. 1 is an equivalent fraction that already has 1 the LCD as its denominator. 1. multiples of 0: 0, 0, 0,,,,, 0 multiples of 0: 0,, 0 0 is the LCD. _ _ _ 0 _ 0 1. multiples of :,, 1 multiples of :, 1 1 is the LCD. 1 _ multiples of :,,,,, 1 multiples of :,,, 1 multiples of :,, 1 1 is the LCD. c multiples of :, 1, 1,... 0,, multiples of :, 1,,,,,, multiples of :,, The LCD is. c. _ multiples of :,,, 1,...,, multiples of :, 1,,, multiples of 1: 1, 0, The LCD is. c _ multiples of :,, 1,... 0,, multiples of :, 1, 1,, 0,,, multiples of 1: 1,, The LCD is. c multiples of :,, 1, 0 multiples of :, 0 multiples of 0: 0 The LCD is 0. Instructor s Manual for Math Dosage Calculations for Health Care

7 c is an equivalent fraction that already has 0 the LCD as its denominator. 0. multiples of :, 1, 1,,..., 11, multiples of :,,,, multiples of 0: 0, 0, The LCD is. c _ 0 1- Comparing Fractions _ , therefore , therefore 0 0 1, therefore , therefore 1. The LCD is , therefore 1. The LCD is _ 1 1. _ 0 1. _ 1 1, therefore 1 1, therefore , therefore , therefore _ 1 1, therefore , therefore _ 1 0 _ _ 1 0, therefore 1 1 Compare the fractions. 1 1 _ 1 1, therefore 1 1. The LCD of,,, is 0. _ _ 1 0 _ 1 0 _ 0 0 _ 0 0 _ 1 0, therefore _ 0 _ _ 1 0 _ 0 0 Instructor s Manual for Math Dosage Calculations for Health Care

8 1. The LCD of,,, is 1. _ _ 1 1 _ _ 1, therefore (1 1) ( ) 1 The LCD of 1,,, is _ _ 00 0 _ 1 0_ 0 0 0, therefore 1 1 ( ) 1 1 _ 11 The LCD of,,, is _ 0_ 1 1 1, therefore 1 _ _ 0 1 ( 1) 1 0. The LCD of,,, is 0. _ _ 1 0 _ 0 _ 0 0 _ Compare _ 0, therefore with. The LCD is _ 1 0 0_ _ 1 0 _ 1 0 tbs is a larger dose than tbs, the amount the patient took. The patient took too little medication.. solution you want: units of medication units of water 1 already-prepared solution: units of medication units of water Compare the fractions. The LCD is 1. _ You can use units of the already-prepared solution.. North wing: patients with high blood pressure total patients 1 South wing: patients with high blood pressure total patients 1 Compare the fractions. The LCD is 0. 1 _ 0 0 0_ 1 0 1, therefore _ 0 The north wing has a larger portion of patients with high blood pressure.. George receives medication once every hours: Martha receives medication times every day: The LCD is. 1 Martha receives medication more often (1 ) (1 1) The LCD of 1 is 1. 1 Instructor s Manual for Math Dosage Calculations for Health Care

9 1 _ 1, therefore You have more time until your shift starts. 1- Adding Fractions _ _ _ _ _ _ The sum of the whole numbers is.. The sum of the whole numbers is The sum of the whole numbers is The sum of the whole numbers is _ 1 1. The sum of the whole numbers is The sum of the whole numbers is _ _ _ 0 0 _ _ _ _ _ 1 1 _ 0 _ 0 0 Instructor s Manual for Math Dosage Calculations for Health Care

10 Add _ 1 0 The sum of the whole numbers is pounds The patient weighed pounds.. Add The sum of the whole numbers is oz of the solution has been used.. Add 1 The sum of the whole numbers is Kelly had cups of liquid.. Add _ You gave your patient tablespoons of medication.. Add 1 The sum of the whole numbers is Your patient slept 1 hours Subtracting Fractions 1. Subtract the whole numbers: Subtract the fractional part: so that Borrow one unit: 1 Instructor s Manual for Math Dosage Calculations for Health Care

11 so that Borrow one unit: so that _ so that _ _ 0 so that 0 1 so that 0 1 so that 1 1 Borrow one unit: _ _ 1 so that _ 1 so that Borrow one unit: 1 0_ _ _ so that 1 1 Borrow one unit: so that (beginning amount) (amount patient drinks) cup remains.. 1 (beginning amount) (amount remaining) 1 1 The patient drank cup.. (medication at start of day) (amount remaining) bottles of medication were used during the day.. First find the total amount of weight that Brenda lost. Add the whole numbers: Add the fractions: 1 Instructor s Manual for Math Dosage Calculations for Health Care 11

12 Brenda lost 1 pounds. Now subtract: 1 (starting weight) (weight loss): Brenda now weighs 1 pounds.. 1 (patient s temp) (normal temp) 1 so that 1 1 Borrow one unit: The patient s temperature is degrees above normal. 1- Multiplying Fractions _ _ 1 _ _ _ 1 1 _ _ 0 _ _ _ _ _ Multiply doses bottles _ 1 bottle doses are available. 1. Multiply the amount of medication per tablet by the number of tablets per dose by the number of doses per day The patient receives 1 grains of medication each day. 1 Instructor s Manual for Math Dosage Calculations for Health Care

13 . 1 1 The patient should have taken 1 tea- spoons per day. 1 The patient took teaspoon per day. c The patient took teaspoon less than 1 prescribed.. 1 0_ The patient took 0 ounces over the four days _ _ tablets contain 10 mg. 1- Dividing Fractions _ _ tablets 0 0_ 1 1 tablet per dose _ 1 The bottle contains doses.. milliliters milliliters per dose _ 1 _ 1 0 _ 0_ The bottle contains 0 doses.. glasses glass The patient should drink 1 times. glass of water Instructor s Manual for Math Dosage Calculations for Health Care 1

14 . ounces 1 ounces per vial _ The case holds vials There are 1 _ 1 1 periods of h in h. 1- Working With Decimals 1. Two-tenths is 0.. Seventeen-hundredths is 0.1. is ones tenths, or.. 1 is ones, 1 tenth, hundredths, 0 or.1. is 0 ones, 0 tenths, 0 hundredths, 00 thousths, or The whole numbers are the same. The tenths place digits are the same. In the hundredths place, 0 so that The first four digits, 0.01, are the same in both numbers. In the ten-thousths place, 0 so that There are no whole numbers. In the tenths place, so that The whole numbers are the same. In the tenths place, so that The whole numbers are the same. In the tenths place, so that.. 1. There are no whole numbers. In the tenths place so that There are no whole numbers. In the tenths place so that There are no whole numbers. The numbers in the tenths place are the same. In the hundredths place so that There are no whole numbers. In the tenths place so that is 0 ones, 0 tenths, hundredths, 00 thousths, or 0.0. is ones, 0 tenths, hundredths, 00 thousths, or.0. _ 11 is ones, 1 tenth, hundredths, 00 1 thousth, or.11. The whole number is the same. In the tenths place, 0 so that..0. The whole numbers are the same. In the tenths place, 1 so that There are no whole numbers. In the tenths place, so that Critical Thinking on the Job: Rounding Errors with : Because the health care professional forgets to carry a unit from the tenths place into the ones place, an error results. The patient does not receive a full dose of medication. With correct rounding, the patient should receive.0 ml, not.0 ml Rounding Decimals 1. The digit to the right of the tenths place is. Do not change the digit in the tenths place: 1.. The digit to the right of the tenths place is. Round the digit in the tenths place up one unit:.. The digit to the right of the tenths place is. Round the digit in the tenths place up one unit: 0. 1 Instructor s Manual for Math Dosage Calculations for Health Care

15 . The digit to the right of the tenths place is. Round the digit in the tenths place up one unit: 0.. The digit to the right of the tenths place is 0. Do not change the digit in the tenths place: 1. The digit to the right of the tenths place is 0. Do not change the digit in the tenths place: 0.. The digit to the right of the tenths place is. Round the digit in the tenths place up one unit: 1.. The digit to the right of the hundredths place is. Do not change the digit in the hundredths place:.. The digit to the right of the hundredths place is. Round the digit in the hundredths place up one unit:.1. The digit to the right of the hundredths place is. Round the digit in the hundredths place up one unit: The digit to the right of the hundredths place is. Round the digit in the hundredths place up one unit:.1 1. The digit to the right of the hundredths place is. Round the digit in the hundredths place up one unit:. 1. The digit to the right of the hundredths place is. Round the digit in the hundredths place up one unit. Since that digit is will round up to 0, carry 1 to the tenths place. Again, the digit there is ; when you add 1, you will write 0 carry 1 to the ones place. Thus, 11. rounded to the hundredths place is 1 1. The digit to the right of the hundredths place is. Round the digit in the hundredths place up one unit:. 1. The digit to the right of the ones place is. Do not change the digit in the ones place: The digit to the right of the ones place is. Round the digit in the ones place up one unit, carry one to the tenths place: 1. rounds to 0 1. The digit to the right of the ones place is 0. Do not change the digit in the ones place: 1. The digit to the right of the ones place is. Round the digit in the ones place up one unit: 1 1. The digit to the right of the tenths place is. Round the digit in the tenths place up one unit. Draw. milliliters of medication into the syringe. 0. Since 0. is already in hundredths, the syringe is calibrated in hundredths, no rounding is necessary. Draw 0. milliliters into the syringe. 1-1 Converting Fractions Into Decimals ( ) (1 ) ( ) 0.. Instructor s Manual for Math Dosage Calculations for Health Care 1

16 1. (1 ) _ ( ) Converting Decimals Into Fractions 1. The number 1 to the left of the decimal point is the whole number. The number to the right of the decimal point is the numerator. is in the tenths place so that is the denominator The number to the left of the decimal point is the whole number. The number to the right of the decimal point is the numerator. is in the tenths place so that is the denominator has no whole number., in the tenths place, is the numerator with a denominator of so that has no whole number. is the numerator. is in the thousths place so that 0. _ 1 00 _ 00. is the whole number. is the numerator. It is in the hundredths place so that has no whole number. 01 is the numerator. 1 is in the thousths place so that 0.01 _ is the whole number. is the numerator. It is in the hundredths place so that is the whole number. 0 is the numerator. 0 is in the thousths place so that _ is the whole number. is the numerator. is in the hundredths place so that. _ 1 0. is the whole number. is the numerator. The last is in the hundredths place so that. _ Adding Subtracting Decimals Instructor s Manual for Math Dosage Calculations for Health Care

17 Steve s temperature had dropped 1. degrees Fahrenheit.. $ $.. First determine how much you have already given your patient... so that: Now subtract. from to find the remaining amount of grams: You still need to give the patient. or grams.. First add You have used 1. ml thus far. Subtract this amount from 0 ml to find the amount remaining in the bottle: The bottle still contains. ml of medication.. First determine the total amount of weight gained by the patient: The patient has gained.0 kg. Add this amount to the original weight: The patient s current weight is. kg. 1-1 Multiplying Decimals The factors have decimal places Instructor s Manual for Math Dosage Calculations for Health Care 1

18 The factors have decimal places The factors have decimal places The factors have decimal places The factors have decimal places The factors have decimal places. 0 Insert zeros: The factors have decimal places. 0 Insert zeros: The factors have decimal places The factors have decimal places The factors have decimal places The factors have decimal places. 0 0 Insert zeros: 0.00 After placing the decimal point, you can drop the final zero: The factors have decimal places. 0 Insert zeroes: The factors have decimal places Multiply. milliliters per dose doses per day:. The factors have 1 decimal place.. The patient receives. milliliters per day milliliters per dose doses per day days. First multiply without the decimal points: The factors have a total of decimal places. Place the decimal point places to the left:. The patient receives. milliliters of medication. 1. First convert 1 to decimal form Multiply without the decimal points: 0. milligrams per tablet 1. tablets per dose doses per day: 1 11 The factors have a total of decimal places. Place the decimal point places to the left: 1.1 The patient receives 1.1 milligrams per day. 1. First convert to decimal form. 0. Multiply without the decimal points: 0. milligrams per tablet 0. tablets per dose doses per day 00 1 Instructor s Manual for Math Dosage Calculations for Health Care

19 The factors have a total of decimal places. Place the decimal point places to the left: The patient receives 0. milligrams per day The factors have decimal places The factors have decimal places After placing the decimal point, 000 you can drop the final zero: The factors have decimal places: After placing the decimal point, you 1 can drop the final zero: 11. Each case contains 11. oz of isopropyl alcohol. Critical Thinking on the Job: Placing Decimals Correctly: The health care professional got confused when placing the decimal in the answer. She followed the rule for addition rather than that for multiplication of decimals. The result, had the error not been caught, would have been a disastrous overdose. The baby should have received 1. g of medication, which rounds to 1. g. 1-1 Dividing Decimals _ _ _. 0. _ 1 _ 1 _ _ _ _ 1.. _ _ rounded to _ _ _ 0.. _ 00 0 _ rounded to _ rounded to , _ 0. (rounded to thousths) _ 1.1 (rounded to thousths) 1. Divide the number of milliliters in the bottle by the number of milliliters in a dose: _ _ 0 The bottle contains 0 doses of medication. 1. Divide the number of ounces in the bottle by the number of ounces in a dose: _ 0 0 The bottle contains 0 doses of medication. 1. The patient received doses per day for days, or a total of doses. Now divide the total amount of medication by the number of doses:. _. 0. Each dose contains 0. grains of medication. 0. Divide the desired weight loss by the number of months: The patient should lose. pounds per month. Instructor s Manual for Math Dosage Calculations for Health Care 1

20 _ _. _ C HAPTER 1 H OMEWORK S OLUTIONS. 1 remainder 1. multiples of :,, 1 multiples of :, 1 1 is the LCD _ 1 1. multiples of :,, 1, 0,, 0,, 0,, 0,, 0 multiples of :,,, 1, 1, 1, 1,,, 0,,,,,,, 1,,, 0 multiples of :,,, 1, 1, 0,,,,, 0,,,,, 0 0 is the LCD _ _ 0 1 Therefore. 1 1 Therefore _ _ _ _ _ 11 1 _ rounded to nearest hundredth is Instructor s Manual for Math Dosage Calculations for Health Care

21 . 1. rounded to nearest hundredth is rounded to the nearest tenth is rounded to the nearest tenth is rounded to the nearest whole number is rounded to the nearest whole number is _ _ _ _ _ _. 1. _ total fluid consumed 1 0 cups 1 0_ 0_ _ 0_ _ 0 1 _ 0 0_ 0_ _ 0 total fluid. cups cups CHAP TER 1 REVIEW _ 1 1 _ Instructor s Manual for Math Dosage Calculations for Health Care 1

22 . _ 1. _ _. is the LCD. already has the LCD _ _ already has the LCD is the LCD is the LCD. c is the LCD. c _ 0 _ _ _ _ 1 so that _ 1 so that 1 1 _ _ 0_ already has the LCD. Compare the fractions: 0 1 _ 0, therefore 1 _ 1 so that 1 0_ already has the LCD Instructor s Manual for Math Dosage Calculations for Health Care _ 1 _ already has the LCD _ _ already has the LCD. _ 1 _

23 0. _ _ _ _ The whole number is the same. In the tenths place, 0 so that..0. The whole number 0 the tenths place 0 are the same. In the hundredths place, 0 so that The whole number the tenths place are the same. The remaining numbers are 0 so that..00. The whole number is the same. In the tenths place, 0 so that.0.0. The digit to the right of the hundredths place is. Round the digit in the hundredths place up one unit: 0.. The digit to the right of the hundredths place is 1. Do not change the digit in the hundredths place:.0. The digit to the right of the hundredths place is 1. Do not change the digit in the hundredths place: 0. The digit to the right of the hundredths place is. Round the digit in the hundredths place up one unit:. 1. The digit to the right of the tenths place is. Do not change the digit in the tenths place:.. The digit to the right of the tenths place is. Round the digit in the tenths place up one unit:.. The digit to the right of the tenths place is. Round the digit in the tenths place up one unit. Because that digit is will round up to 0, carry 1 to the ones place:.0. The digit to the right of the tenths place is. Round the digit in the tenths place up one unit: 0.1. The digit to the right of the ones place is. Round the digit in the ones place up one unit:. The digit to the right of the ones place is. Round the digit in the ones place up one unit: 1. The digit to the right of the ones place is. Round the digit in the ones place up one unit: 1. The digit to the right of the ones place is. Do not change the digit in the ones place: has no whole number. is the numerator. is in the hundredths place: has no whole number. is the numerator. is in the hundredths place: is the whole number. is the numerator. is in the tenths place:.. 1 is the whole number. 1 is the numerator. 1 is in the thousths place: Instructor s Manual for Math Dosage Calculations for Health Care

24 The factors have decimal places The factors have decimal places The factors have decimal places The factors have decimal places _ _ Type O: 1 Type AB: _ _ 0 Type A: 1 Type B: 1. The patient receives cup twice or cup. The patient should receive cup. The patient receives cup too little.. 1 Brian drank cups of liquid during the day The bottle contains doses _ 0 1 The bottle contains 0 doses. Critical Thinking Convert all the diameters to measures with a common denominator. 1 is the LCD All the instruments from 1 tray except for the one that is through are on the 1 instruments in order are 1,, 1,, Case Study 1. The remaining,,. 1 1 From Day 1 to Day, the patient s weight increases by pounds. From Day to Day at :00 m., the patient s weight increases by pounds. During the day, the patient s weight decreases by pound. From Day at :00 p.m. to Day at :00 m., the patients weight decreases by 1 1 pounds. During Day, the patient s weight decreases again, by 1 pounds. Internet Activity Pages on the Internet change frequently. Any URLs listed may have been removed from the Internet by the time you use this text. The web sites you might find using search engines include: Web sites such as these, which provide dosage information about medications, can help you practice your calculation skills prepare for exams. Remember to evaluate any site you are using for accuracy legitimacy. Instructor s Manual for Math Dosage Calculations for Health Care